Question: A circle has a circumference of $16\pi$. It has an arc of length $\dfrac{20}{3}\pi$. What is the central angle of the arc, in radians? ${16\pi}$ ${\dfrac{5}{6}\pi}$ $\color{#DF0030}{\dfrac{20}{3}\pi}$
Explanation: The ratio between the arc's central angle $\theta$ and $2 \pi$ radians is equal to the the ratio between the arc length $s$ and the circle's circumference $c$ $\dfrac{\theta}{2 \pi} = \dfrac{s}{c}$ $\dfrac{\theta}{2 \pi} = \dfrac{20}{3}\pi \div 16\pi$ $\dfrac{\theta}{2 \pi} = \dfrac{5}{12}$ $\theta = \dfrac{5}{12} \times 2 \pi$ $\theta = \dfrac{5}{6}\pi$ radians